The dimension down scaling capability of the silicon based transistors has produced significant developments in the electronic industry. The channel length reduction has been accompanied by many limitations and challenges in the performance of the transistor. According to the ITRS and Moore law silicon based technology is near to its end, consequently the novel material innovations are needed in the near future. The graphene based material is the promising candidate for silicon channel replacement in conventional transistor. In this paper, graphene, graphene nanoribbons and their fundamental properties such as mechanical, electrical and electronic specifications are introduced. Then, graphene nanoribbon field effect transistor and its modeling and simulation methods are investigated. The best method for device simulation is the self-consistent solving of Poisson and Schrödinger equations under non-equilibrium green's function with the tight binding approximation. In order to investigate the effect of down scaling on the transistor performance, parameters such as drain induced barrier lowering, sub-threshold swing, $I_{ON}/I_{OFF}$ratio, and transconductance are studied. Moreover, utilizations of the graphene nanoribbon field effect transistor including circuit-based, high frequency, and biosensors applications are introduced. The results show that graphene based transistors are an excellent replacement to silicon based transistors.

硅基晶体管的尺寸缩小能力已经在电子工业中产生了重大发展。沟道长度的减小伴随着晶体管性能的许多限制和挑战。根据ITRS和摩尔定律，基于硅的技术已接近尾声，因此在不久的将来需要新颖的材料创新。石墨烯基材料是常规晶体管中硅通道替代的有前途的候选者。本文介绍了石墨烯，石墨烯纳米带及其基本性能，如机械，电气和电子规格。然后，研究了石墨烯纳米带场效应晶体管及其建模和仿真方法。进行设备仿真的最佳方法是在非平衡格林函数下通过紧密绑定近似对Poisson和Schrödinger方程进行自洽求解。为了研究缩小对晶体管性能的影响，使用了诸如漏极引起的势垒降低，亚阈值摆幅，${\mathrm{一世}}_{Øñ}/{\mathrm{一世}}_{ØFF}$比率和跨导的研究。此外，介绍了石墨烯纳米带场效应晶体管的利用，包括基于电路的，高频的和生物传感器的应用。结果表明，基于石墨烯的晶体管是硅基晶体管的出色替代品。